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Research Article | Open Access

Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations

Gennaro Ciampa1, Gianluca Crippa2, Stefano Spirito1( )
DISIM–Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi dell'Aquila, Via Vetoio, L'Aquila 67100, Italy
Departement Mathematik Und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland
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Abstract

The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with Lp initial vorticity, provided that p≥4. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order |log⁡ν|−α/2 with α>0.

Keywords

incompressible Euler equationsvorticitypropagation of regularitymodulus of continuityinviscid limit

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Mathematics in Engineering
Volume 6 Issue 4,
August 2024
Pages 494-509
DOI: 10.3934/mine.2024020

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Ciampa G, Crippa G, Spirito S. Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations. Mathematics in Engineering, 2024, 6(4): 494-509. https://doi.org/10.3934/mine.2024020

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Received: 12 February 2024
Revised: 24 June 2024
Accepted: 25 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)